A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 38
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Rubinstein, Ed., Marcel Dekker, New York, 1995,Chap. 2.23. N. Koizumi and S. Aoyagui, /. Electroanal.Chem., 55, 452 (1974).24. H. Kojima and A. J. Bard, /. Am. Chem. Soc,97,6317(1975).25. K. J. Vetter, op. cit., Chap. 4.26. T. Erdey-Gruz, op. cit., Chap. 4.27. P. Delahay, "Double Layer and Electrode Kinetics," op. cit., Chap. 10.28. N. Tanaka and R. Tamamushi, Electrochim.Acta, 9, 963 (1964).29. В. Е. Conway, "Electrochemical Data," Elsevier, Amsterdam, 1952.30. R. Parsons, "Handbook of ElectrochemicalData," Butterworths, London, 1959.48. M. J. Weaver in "Comprehensive Chemical Kinetics,"' R. G. Compton, Ed., Elsevier, Amsterdam, Vol. 27, 1987. Chap.
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MacLean, E. Lam, Y. Chong, G. T. Olsen, JLuo, M. Gozin, and J. F. Kayyem, /. Am. Chem.Soc, 111, 1059 (1999).3.8 PROBLEMS3.1 Consider the electrode reaction О + ne «^ R. Under the conditions that CRR = C o = 1 mM,k° = 10~7 cm/s, a = 0.3, and n = 1:(a) Calculate the exchange current density, jo = IQ/A, in fiA/cm2.(b) Draw a current density-overpotential curve for this reaction for currents up to 600 /лА/ст2 anodic and cathodic.
Neglect mass-transfer effects.(c) Draw log \j\ vs. 7) curves (Tafel plots) for the current ranges in (b).3.2 A general expression for the current as a function of overpotential, including mass-transfer effects,can be obtained from (3.4.29) and yields1~ iexpt-a/rj] - exp[(l - a)fr]]exp[(l - a)frj\| exp[- afq](a) Derive this expression.(b) Use a spreadsheet program to repeat the calculation of Problem 3.1, parts (b) and (c), includingthe effects of mass transfer. Assume m0 - mR= 10~3 cm/s.3.3 Use a spreadsheet program to calculate and plot current vs. potential and ln(current) vs. potential forthe general i-iq equation given in Problem 3.2.(a) Show a table of results [potential, current, ln(current), overpotential] and graphs of / vs.
17 andln|/| vs. 7] for the following parameters: A = 1 cm 2 ; C o = 1.0 X 10~3 mol/cm3; C R = 1.0 X10" 5 mol/cm3; n = 1; a = 0.5; k° = 1.0 X 10" 4cm/s; m o = 0.01 cm/s; mR= 0.01 cm/s; E° = -0.5 V vs. NHE.(b) Show the i vs. E curves for a range of k° values with the other parameters as in (a). At what values of к0 are the curves indistinguishable from nernstian ones?(c) Show the / vs. E curves for a range of a values with the other parameters as in (a).3.4 In most cases, the currents for individual processes are additive, that is, the total current, /t, is givenas the sum of the currents for different electrode reactions (/1? 12, /3,..
. ) . Consider a solution with aPt working electrode immersed in a solution of 1.0 M HBr and 1 mM K 3 Fe(CN) 6 . Assume the following exchange current densities:H + /H 2Br2/Br~Fe(CN)^/Fe(CN)£-70 = 10~3 A/cm2j 0 = 10~2 A/cm2j 0 = 4 X 10~5 A/cm23.8 Problems135Use a spreadsheet program to calculate and plot the current-potential curve for this systemscanning from the anodic background limit to the cathodic background limit.
Take the appropriate standard potentials from Table C.I and values for other parameters (ra 0 , a, . . . ) fromProblem 3.3.3.5 Consider one-electron electrode reactions for which a = 0.50 and a = 0.10. Calculate the relativeerror in current resulting from the use in each case of:(a) The linear i—r) characteristic for overpotentials of 10, 20, and 50 mV.(b) The Tafel (totally irreversible) relationship for overpotentials of 50, 100, and 200 mV.3.6 According to G. Scherer and F. Willig [/.
Electroanal Chem., 85, 77 (1977)] the exchange current2density, j 0 , for Pt/Fe(CN)^~ (2.0 mM), Fe(CN)^" (2.0 mM), NaCl (1.0 M) at 25°C is 2.0 mA/cm .The transfer coefficient, a, for this system is about 0.50. Calculate (a) the value of k°; (b)y'o for a solution 1 M each in the two complexes; (c) the charge-transfer resistance of a 0.1 cm electrode in asolution 10~4 M each in ferricyanide and ferrocyanide.3.7 Berzins and Delahay [/.
Am. Chem. Soc, 11, 6448 (1955)] studied the reactionCd 2 + + 2e ^ Cd(Hg)and obtained the following data with Ccd(Hg) = ®'^® ^CCd2+(mM)1.0;o (mA/cm2)30.0:0.5017.30.2510.10.104.94(a) Assume that the general mechanism in (3.5.8)-(3.5.10) applies. Calculate n' + a, and suggestvalues for n', n'\ and a individually. Write out a specific chemical mechanism for the process.(b) Calculate k%p.(c) Compare the outcome with the analysis provided by Berzins and Delahay in their originalpaper.3.8 (a) Show that for a first-order homogeneous reaction,A-IBthe average lifetime of A is l/kf.(b) Derive an expression for the average lifetime of the species О when it undergoes the heterogeneous reaction,Note that only species within distance d of the surface can react. Consider a hypothetical system in which the solution phase extends only d (perhaps 10 A) from the surface,(c) What value of kf would be needed for a lifetime of 1 ms? Are lifetimes as short as 1 ns possible?3.9 Discuss the mechanism by which the potential of a platinum electrode becomes poised by immersion into a solution of Fe(II) and Fe(III) in 1 M HCl.
Approximately how much charge is required toshift the electrode potential by 100 mV? Why does the potential become uncertain at low concentrations of Fe(II) and Fe(III), even if the ratio of their concentrations is held near unity? Does this experimental fact reflect thermodynamic considerations? How well do your answers to these issuesapply to the establishment of potential at an ion-selective electrode?3.10 In ammoniacal solutions ([NH 3 ] ~ 0.05 M), Zn(II) is primarily in the form of the complex ionZn(NH 3 ) 3 (OH) + [hereafter referred to as Zn(II)]. In studying the electroreduction of this compound to zinc amalgam at a mercury cathode, Gerischer [Z.
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